n. a subset of a given group, written aH or Ha, whose members are the products of a given element, a, of the group with a given subgroup, H. The cosets of H in G are disjoint and form a partition of G. The left and right cosets, aH and Ha, may be distinct in a non-commutative group, and if aH = Ha for all a in G, then H is said to be normal in G. See also transversal.